The e-commerce giant is set to broaden its same-day shipping service starting Thursday by allowing later ordering times in some places and adding Dallas and San Francisco to the dozen cities where it’s available.

As well, Amazon will make it easier to find the roughly one million items that are eligible for same-day delivery, by adding search filters and a new section to the website for its “Local Express Delivery” service. It also is lowering the delivery fee for many orders made by members of its $99 Prime unlimited shipping program.

For Amazon and other e-commerce companies, same-day delivery has long been viewed as a key obstacle in their effort to tackle brick-and-mortar retailers. Despite nearly limitless inventory, online retailers haven’t yet found a way to feasibly roll out same-day delivery for a broad swath of Americans.

More than four years after introducing same-day delivery, Amazon’s service is unavailable in the vast majority of the country.

The Wall Street Journal reported last week that Amazon is testing out a delivery service of its own that could help it expand same-day shipping. The company is bypassing UPS, FedEx and the Postal Service, among other carriers, by bringing Amazon packages directly to customers’ doorsteps in San Francisco, Los Angeles, New York and possibly elsewhere.

As well, it introduced same-day fresh grocery delivery in Los Angeles and San Francisco last year after testing it for years in its hometown, Seattle.

While Amazon is expanding same-day delivery, it is ending the service in Las Vegas, an original site for the service and where Amazon operates a shipping warehouse just north of the city. A spokeswoman said that the company is always testing new services and delivery areas, but declined to discuss why Las Vegas is losing its same-day delivery.

In San Francisco, Phoenix and some other cities, customers can place an order as late as 12:15 p.m. and get it by 9 p.m. that night. Until recently, Phoenix residents had to place orders by 9:30 a.m. to get it the same day.

Amazon Prime members in San Francisco, Phoenix, Seattle, Dallas and Los Angeles and, later, other markets, will pay a flat $5.99 fee for same-day delivery for up to about 150 pounds of goods. The fee had previously been $3.99 for each item.